1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Modular Arithmetic

  1. Jul 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that if a = (b mod m) and c = d(mod m) and m => 2, then a - c = (b - d)(mod m)

    2. Relevant equations

    c = d(mod m) <=> m|(c - d)
    d = c + xm

    3. The attempt at a solution

    I don't know how any equivalences for a = (b mod m), is there a way to get b from a = (b mod m)?

    I had a + c = (b mod m) + d(mod m) but I'm not sure where to go from there
     
  2. jcsd
  3. Jul 11, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    a= b (mod m) means that a- b is divisible by m or that a- b= mp for some integer p.
    Similarly, c= d (mod m) means that c- d= mq for some integer q.

    Now what does a-c= b- d (mod m) mean?
     
  4. Jul 11, 2008 #3
    a - c = (b - d)(mod m) would be (a - c) - (b - d) = mx for some x

    But its a = (b mod m)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook